
This is a classical stability assumption on a pair potential; see [1]}.
Let \(\alpha >0\)  and assume that \(\kappa \)  is given by
\(\kappa (x,\mu )=\alpha \exp \bigg [-\int U(x,y)\,\mu (\mathrm {d}y)\bigg ],\quad x \in {\mathbb {X}},\,\mu \in \mathbf {N},\) 
